Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples
Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computa...
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| Autor*in: |
Sutradhar, Brajendra C. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
Conditional means for non-sampled units doubly weights composed of sampling and correlation weights |
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| Anmerkung: |
© Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Sankhya - Springer India, 1961, 85(2022), 2 vom: 24. Okt., Seite 1452-1488 |
|---|---|
| Übergeordnetes Werk: |
volume:85 ; year:2022 ; number:2 ; day:24 ; month:10 ; pages:1452-1488 |
| Links: |
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| DOI / URN: |
10.1007/s13171-022-00297-0 |
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OLC2144627517 |
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| 520 | |a Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. | ||
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| 650 | 4 | |a multinomial proportions | |
| 650 | 4 | |a random cluster effects | |
| 650 | 4 | |a two-stage cluster sample. | |
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10.1007/s13171-022-00297-0 doi (DE-627)OLC2144627517 (DE-He213)s13171-022-00297-0-p DE-627 ger DE-627 rakwb eng 310 VZ Sutradhar, Brajendra C. verfasserin aut Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. Conditional means for non-sampled units cluster correlation effect consistency doubly weights composed of sampling and correlation weights doubly weighted conditional likelihood estimating equations multinomial proportions random cluster effects two-stage cluster sample. Enthalten in Sankhya Springer India, 1961 85(2022), 2 vom: 24. Okt., Seite 1452-1488 (DE-627)129474665 (DE-600)203149-8 (DE-576)014853116 0581-572X nnns volume:85 year:2022 number:2 day:24 month:10 pages:1452-1488 https://doi.org/10.1007/s13171-022-00297-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4266 AR 85 2022 2 24 10 1452-1488 |
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10.1007/s13171-022-00297-0 doi (DE-627)OLC2144627517 (DE-He213)s13171-022-00297-0-p DE-627 ger DE-627 rakwb eng 310 VZ Sutradhar, Brajendra C. verfasserin aut Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. Conditional means for non-sampled units cluster correlation effect consistency doubly weights composed of sampling and correlation weights doubly weighted conditional likelihood estimating equations multinomial proportions random cluster effects two-stage cluster sample. Enthalten in Sankhya Springer India, 1961 85(2022), 2 vom: 24. Okt., Seite 1452-1488 (DE-627)129474665 (DE-600)203149-8 (DE-576)014853116 0581-572X nnns volume:85 year:2022 number:2 day:24 month:10 pages:1452-1488 https://doi.org/10.1007/s13171-022-00297-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4266 AR 85 2022 2 24 10 1452-1488 |
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10.1007/s13171-022-00297-0 doi (DE-627)OLC2144627517 (DE-He213)s13171-022-00297-0-p DE-627 ger DE-627 rakwb eng 310 VZ Sutradhar, Brajendra C. verfasserin aut Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. Conditional means for non-sampled units cluster correlation effect consistency doubly weights composed of sampling and correlation weights doubly weighted conditional likelihood estimating equations multinomial proportions random cluster effects two-stage cluster sample. Enthalten in Sankhya Springer India, 1961 85(2022), 2 vom: 24. Okt., Seite 1452-1488 (DE-627)129474665 (DE-600)203149-8 (DE-576)014853116 0581-572X nnns volume:85 year:2022 number:2 day:24 month:10 pages:1452-1488 https://doi.org/10.1007/s13171-022-00297-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4266 AR 85 2022 2 24 10 1452-1488 |
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10.1007/s13171-022-00297-0 doi (DE-627)OLC2144627517 (DE-He213)s13171-022-00297-0-p DE-627 ger DE-627 rakwb eng 310 VZ Sutradhar, Brajendra C. verfasserin aut Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. Conditional means for non-sampled units cluster correlation effect consistency doubly weights composed of sampling and correlation weights doubly weighted conditional likelihood estimating equations multinomial proportions random cluster effects two-stage cluster sample. Enthalten in Sankhya Springer India, 1961 85(2022), 2 vom: 24. Okt., Seite 1452-1488 (DE-627)129474665 (DE-600)203149-8 (DE-576)014853116 0581-572X nnns volume:85 year:2022 number:2 day:24 month:10 pages:1452-1488 https://doi.org/10.1007/s13171-022-00297-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4266 AR 85 2022 2 24 10 1452-1488 |
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10.1007/s13171-022-00297-0 doi (DE-627)OLC2144627517 (DE-He213)s13171-022-00297-0-p DE-627 ger DE-627 rakwb eng 310 VZ Sutradhar, Brajendra C. verfasserin aut Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. Conditional means for non-sampled units cluster correlation effect consistency doubly weights composed of sampling and correlation weights doubly weighted conditional likelihood estimating equations multinomial proportions random cluster effects two-stage cluster sample. Enthalten in Sankhya Springer India, 1961 85(2022), 2 vom: 24. Okt., Seite 1452-1488 (DE-627)129474665 (DE-600)203149-8 (DE-576)014853116 0581-572X nnns volume:85 year:2022 number:2 day:24 month:10 pages:1452-1488 https://doi.org/10.1007/s13171-022-00297-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4266 AR 85 2022 2 24 10 1452-1488 |
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Sutradhar, Brajendra C. |
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prediction theory for multinomial proportions using two-stage cluster samples |
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Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples |
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Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. © Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. © Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract In a two-stage clusters sampling setup for categorical data, it is well known that the so-called best prediction of the category based proportions involves computing the conditional means of the non-sampled multinomial variables conditional on the sampled multinomial responses. This computation is however not easy mainly due to the complex cluster correlations among multinomial responses within a cluster. The independence assumption based approach or any linear model approach for cluster correlated data those used so far in the existing studies are not valid for the computation of such conditional means in the prediction function for multinomial data. As opposed to these ‘working’ independence or linear models based approaches, in this paper we first develop a cluster correlation structure for multinomial data and exploit this structure to compute theoretically valid formulas for the conditional means of non-sampled hypothetical responses. Next because these conditional means or equivalently the prediction function contains the regression and clustered variance/correlation parameters, we estimate these parameters using the survey sampling weights based conditional likelihood approach, whereas the existing studies mostly use the independence assumption based likelihood or moment approaches which are invalid or inadequate in a correlation setup. The proposed conditional likelihood estimators are shown to be consistent for their respective parameters leading to the consistent estimation of the prediction function for the multinomial proportions. © Indian Statistical Institute 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Prediction Theory for Multinomial Proportions Using Two-stage Cluster Samples |
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